FSSA Detects Decade Long Oscillation that MSSA Cannot

The following plot displays the kernel density estimation functional time series results of the NDVI data.

We run FSSA on the NDVI data and obtain the following plots that suggest we should have three groups for reconstruction. The first group used in reconstruction uses only the first component, the second group should use components two and three, and a fourth group that only uses reconstruction four.

We see a periodicity here of the 16 day periods between capturing images from the NDVI data

Here is the reconstruction using only the first components which gives us trend

Here we see oscillatory behavior in reconstruction that used components 2 and 3 which captures the 16 day periodicity

This is the interesting component that captures roughly decade long oscillations in the data. This is not captured by MSSA. The rest are MSSA results that show that MSSA cannot capture this same fourth component of information that FSSA can capture.

Trend

Oscillatory behavior

MSSA doesn’t capture any interesting behavior in component 4 with small L

Wth large L, MSSA approximated FSSA results as wtih long lags, more of each discretized function is stacked upon one another.

The fourth component is now captured by MSSA for large L

While MSSA can be used to approximate FSSA results, we recommend using FSSA as the data is inherently functional so a functional frame work is more suitable. Instead of applying MSSA to kernel density estimates, we apply MSSA to raw image data.

MSSA applied to raw image data doesn’t expose the decade long oscillation.